Positive and oscillating solutions of differential equations with delay in critical case

https://doi.org/10.1016/S0377-0427(97)00217-3Get rights and content
Under an Elsevier user license
open archive

Abstract

This article is devoted to the problem of existence of positive solution for common classes of nonlinear retarded functional differential equations. Some criteria of its existence are proved, as well as some comparison results. The obtained results are applied to the linear case. Moreover, the existence of positive and oscillating solutions of a differential equation with delay ẋ(t)=−a(t)x(t−τ) in the critical case is considered. Some comparisons with known results are given.

Keywords

Positive solution
Oscillating solution
Nonlinear retarded functional differential equation
Linear differential equation with constant delay
Topological principle of Ważewski (Rybakowski's approach)

MSC

34K15

MSC

34K25

Cited by (0)